YES
Time: 0.001287
TRS:
 {      fib 0() -> 0(),
      fib s 0() -> s 0(),
      fib s s x -> sp g x,
    fib s s 0() -> s 0(),
  sp pair(x, y) -> +(x, y),
          g 0() -> pair(s 0(), 0()),
          g s x -> np g x,
        g s 0() -> pair(s 0(), s 0()),
  np pair(x, y) -> pair(+(x, y), x),
      +(x, 0()) -> x,
      +(x, s y) -> s +(x, y)}
 DP:
  DP:
   {    fib# s s x -> sp# g x,
        fib# s s x -> g# x,
    sp# pair(x, y) -> +#(x, y),
            g# s x -> g# x,
            g# s x -> np# g x,
    np# pair(x, y) -> +#(x, y),
        +#(x, s y) -> +#(x, y)}
  TRS:
  {      fib 0() -> 0(),
       fib s 0() -> s 0(),
       fib s s x -> sp g x,
     fib s s 0() -> s 0(),
   sp pair(x, y) -> +(x, y),
           g 0() -> pair(s 0(), 0()),
           g s x -> np g x,
         g s 0() -> pair(s 0(), s 0()),
   np pair(x, y) -> pair(+(x, y), x),
       +(x, 0()) -> x,
       +(x, s y) -> s +(x, y)}
  EDG:
   {(g# s x -> g# x, g# s x -> np# g x)
    (g# s x -> g# x, g# s x -> g# x)
    (np# pair(x, y) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (fib# s s x -> sp# g x, sp# pair(x, y) -> +#(x, y))
    (g# s x -> np# g x, np# pair(x, y) -> +#(x, y))
    (+#(x, s y) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (sp# pair(x, y) -> +#(x, y), +#(x, s y) -> +#(x, y))
    (fib# s s x -> g# x, g# s x -> g# x)
    (fib# s s x -> g# x, g# s x -> np# g x)}
   SCCS (2):
    Scc:
     {+#(x, s y) -> +#(x, y)}
    Scc:
     {g# s x -> g# x}
    SCC (1):
     Strict:
      {+#(x, s y) -> +#(x, y)}
     Weak:
     {      fib 0() -> 0(),
          fib s 0() -> s 0(),
          fib s s x -> sp g x,
        fib s s 0() -> s 0(),
      sp pair(x, y) -> +(x, y),
              g 0() -> pair(s 0(), 0()),
              g s x -> np g x,
            g s 0() -> pair(s 0(), s 0()),
      np pair(x, y) -> pair(+(x, y), x),
          +(x, 0()) -> x,
          +(x, s y) -> s +(x, y)}
     SPSC:
      Simple Projection:
       pi(+#) = 1
      Strict:
       {}
      Qed
    SCC (1):
     Strict:
      {g# s x -> g# x}
     Weak:
     {      fib 0() -> 0(),
          fib s 0() -> s 0(),
          fib s s x -> sp g x,
        fib s s 0() -> s 0(),
      sp pair(x, y) -> +(x, y),
              g 0() -> pair(s 0(), 0()),
              g s x -> np g x,
            g s 0() -> pair(s 0(), s 0()),
      np pair(x, y) -> pair(+(x, y), x),
          +(x, 0()) -> x,
          +(x, s y) -> s +(x, y)}
     SPSC:
      Simple Projection:
       pi(g#) = 0
      Strict:
       {}
      Qed